Gridding Daily Climate Variables for use in

ENSEMBLES

Malcolm Haylock, Climatic Research Unit

Nynke Hofstra, Mark New, Phil Jones

Overview

• Applications → Scale

• Stochastic or Deterministic

• Methods

• Determining the best method

• Data preprocessing

• Uncertainty

Applications

• Daily P, Tmin, Tmax, SLP, Snow- Precipitation only for now

• Validation of RCMs- What is the true scale of RCMs? - Need to create gridded observations

that are area average

• Analysis of past changes

Stochastic or Deterministic• Stochastic

- obs(x) = z(x) + ε(x)- assume that observed station data are only one of

many possible “realisations” that could have occurred.

- Interpolate using inter-station covariance.• spatial and temporal

- generally don’t reproduce observations (inexact interpolation).

• Deterministic- obs(x) = z(x)- assume that observed station data are the only

possible realisation.- exact interpolation

Why Stochastic?

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 5 10 15 20 25 30 35 40

Distance

Semivariogram

• Variation at the local scale can not be determined using available station network

€

E z(x) − z(x ')[ ] /2

Variogram=E(z(x)-z(x1)](normalised)

Methods

• Kriging

• Thin plate splines

• (Reduced Space) Optimum Interpolation

• Angular Distance Weighting

• Conditional Interpolation

Kriging• Highly developed stochastic method used

extensively in the geosciences.

• obs(x) = z(x) + ε(x), z(x) is an autocorrelated random field calculated as a linear weighted average of surrounding stations.

• Weights determined by statistically modeling the regional variation by fitting an appropriate function to the variogram.

• Variations to handle anisotropy (spatial covariance dependent on orientation), large scale trends and other common problems.

• Statistical model may be different for each day.

Anisotropy

Thin Plate Splines• Stochastic method that fits a surface to the data

using smooth functions of the station separation distance

• Can be considered as a special case of Kriging with a particular class of covariance functions, however these functions are rarely used in Kriging.

• Contains a smoothing parameter which is usually set by cross validation.

• Implicit error estimation by cross validation.

Optimum Interpolation• Stochastic model developed for data assimilation

• Accounts for both spatial and temporal autocorrelation- unlike traditional Kriging and Splines which only

use spatial.- is temporal autocorrelation appropriate for precip.?

• Assumes Gaussian covariance error distribution - one of several models possible in Kriging.

• Reduced Space version uses EOFs to greatly speed calculation and limit dependence on small scale variation.- appropriate for daily precip?

Angular Distance Weighting

• Interpolation of anomalies

• Weight based on distance

and angle

• Stations closest to grid

points have greater weight

• Stations with biggest mean

angle have greater weight

• Elevation not included

• E.g. New et al. 2000, CRU dataset

j

k

l

θ

Grid point

Station

dist

Conditional Interpolation

• So far only interpolation of precipitation

• Interpolation is conditional on synoptic state

• Synoptic state defined with Self Organising Maps

• Interpolation in two steps- Wet or dry target location- If wet: interpolation of magnitude

• Weights regard distance, radial distribution and synoptic state

• Calculation of area mean

• Hewitson and Crane 2005

Selecting the best method(s)

• Cross validation- for all stations, remove the station then

calculate predicted value and evaluate appropriate error statistic (e.g. RMS).

- Assumes predicted value is a point value, but stochastic methods give the expected value and so hopefully the smallest average error.

• Can test models using a region with high station density by omitting stations and comparing with true are average.

Data Preprocessing

• Stochastic methods require Gaussian-distributed data

• Obtain consistency across region by interpolating anomaly from monthly mean (T, SLP) or % of monthly total (P).

• Interpolated results can be applied to previously gridded monthly data that utilise many more stations.

Rainfall Skewnessdaily/month

dry days removed

Uncertainty• Measurement error

• Homogeneity error

• Interpolation error- method• use many methods or best method

- statistical model within method• choose best model but still a

generalisation- station network• cross validation